SSC (English Medium) 10th Standard - Maharashtra State Board Question Bank Solutions

In the given figure `square`ABCD is a square of side 50 m. Points P, Q, R, S are midpoints of side AB, side BC, side CD, side AD respectively. Find area of shaded region

If sin θ + sin² θ = 1 show that: cos² θ + cos⁴ θ = 1

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If length of sides of a triangle are a, b, c and a² + b² = c², then which type of triangle it is?

From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?

In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?

From given figure, In ∆ABC, If AC = 12 cm. then AB =?

Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∴ ∠BAC = `square`

∴ ∆ABC is 30° – 60° – 90° triangle

∴ In ∆ABC by property of 30° – 60° – 90° triangle.

∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC

∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ `square` = 6 and BC = `6sqrt(3)`

Prove the following theorem:

Angles inscribed in the same arc are congruent.

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cos θ. sec θ = ?

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sec 60° = ?

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1 + cot²θ = ? 

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cot θ . tan θ = ?

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sec²θ – tan²θ =?

sin²θ + sin²(90 – θ) = ?

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`(1 + cot^2"A")/(1 + tan^2"A")` = ?

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sin θ = `1/2`, then θ = ?

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tan (90 – θ) = ?

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cos 45° = ?

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Which is not correct formula?

`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?

If tan θ = `13/12`, then cot θ = ?